Unit tangent vectors, Normal vectors, and Gradients

In summary, the speaker is new to Physics Forums and has been using threads as guides for about a year. They are currently studying for their Calc III exam and have come across a lapse in understanding regarding the difference between a tangent and a normal vector. They know that finding at least one of these vectors involves finding the partial derivatives of a given function and using them as components of the gradient function. They are unsure of the difference between a normal vector and a unit tangent vector, and how they relate to each other in terms of a function. They apologize for not using the correct template and ask for clarification on this topic.
  • #1
ChristopherF1
1
0
So I'm kinda new to Physics Forums but I've been using threads as guides for about a year now.

Basically, I'm hardcore studying for my Calc III exam (the final is in a few weeks) and I came across an interesting lapse in my understanding (well many in fact, but one in particular).
First of all I can assume that a tangent and a normal/perpendicular vector are NOT the same thing, yet for some reason they both have pretty much the same characteristics.
I know that finding at least one of them involves finding the partial derivatives of a given function, which then are used as the components of the gradient function (the upside down triangle thing) Right?
And a gradient gives you... the normal vector right? or something regarding the tangent plane at a point, whose normal vector is that of the surface of the function? I could be mistaken but my major malfunction seems to be that I can't differentiate (no math puns please- I'm doing more studying than sleeping) between finding the normal vector and the unit tangent vector, which in practice seem to be the same thing (at least for me.)


(It is at this point where I actually noticed the warning at the top of the page regarding the template I am supposed to use. I apologize, and if a problem arises I'll be glad to repost using the template, which at this point seems pointless...)
 
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  • #2
Anyway, I would really appreciate it if someone could explain the difference between a normal vector and a unit tangent vector, and how they relate to each other, in terms of a function. Thanks in advance!
 

1. What are unit tangent vectors?

Unit tangent vectors are vectors that have a magnitude of 1 and are tangent to a curve or surface at a specific point. They represent the direction of the curve or surface at that point.

2. How are normal vectors defined?

Normal vectors are defined as the vectors that are perpendicular to a surface at a specific point. They are used to determine the orientation of a surface or the direction of motion of a particle on the surface.

3. What is the relationship between unit tangent and normal vectors?

Unit tangent vectors and normal vectors are always perpendicular to each other. This means that the dot product of these two vectors is always equal to 0.

4. How are gradients used in vector calculus?

Gradients are used to represent the rate of change of a function in a particular direction. They are useful in calculating the direction of steepest ascent or descent for a function.

5. Can unit tangent and normal vectors be used in three-dimensional space?

Yes, unit tangent and normal vectors can be used in three-dimensional space. In fact, they are often used to determine the curvature of a curve or surface in three-dimensional space.

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